Multiply and Divide Surd Expressions

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Question 1 of 6

Simplify

$(4sqrt8times2sqrt5)/(8sqrt20)$

1. $3sqrt(2)$
2. $3/4sqrt(2)$
3. $sqrt(2)$
4. $2sqrt(5)$

Question 2 of 6

Simplify

$(8sqrt3times5sqrt6)/(4sqrt18)$

1. $10$
2. $10/sqrt(2)$
3. $36$
4. $36/sqrt(2)$

Question 3 of 6

Simplify

$(4sqrt27timessqrt18)/(sqrt48)$

1. $9sqrt(2)$
2. $32sqrt(2)$
3. $27$
4. $9sqrt(3)$

Question 4 of 6

Simplify

$sqrt(5a^2) xx sqrt(12b^5)$

1. $2ab^2sqrt(15b)$
2. $4a^2b^4sqrt(15b)$
3. $ab^2sqrt(17b)$
4. $2sqrt(15ab^7)$

Question 5 of 6

5. Question
Simplify

$sqrt(7xy^2) xx 5sqrt(x)$
- 1. $5x^2y^2 sqrt(7)$
- 2. $5y sqrt(7x)$
- 3. $xy sqrt35$
- 4. $5xy sqrt7$
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Multiplication Property of Surds

$sqrt(ab)=sqrt(a) xx sqrt(b)$

Combine the surds

$sqrt(7xy^2) xx 5sqrt(x)$ $=$ $5sqrt(7 xx x xx y^2 xx x)$

$=$ $5sqrt(7 xx x^2y^2)$

Take the perfect squares out of the surd by getting their square root

$=$ $5 sqrt7 xx sqrt(x^2) xx sqrt(y^2)$ Simplify

$=$ $5sqrt7 xx x xx y$

$=$ $5xy sqrt7$

$5xy sqrt7$
Question 6 of 6

6. Question
Simplify

$sqrt(\frac{45x^3}{5x^2})$
- 1. $9sqrt(x)$
- 2. $3sqrt(x^{3/2})$
- 3. $3sqrt(x)$
- 4. $sqrt(3x^3/2)$
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Division Property of Surds

$sqrt(a/b)=sqrt(a) / sqrt(b)$

Write as a division of separate surds

$sqrt(\frac{45x^3}{5x^2})$ $=$ $\frac{sqrt(45) xx sqrt(x^3)}{sqrt(5) xx sqrt (x^2)}$

Divide the numbers and the variables separately

Divide the numbers

$sqrt(45) / sqrt(5)$ $=$ $sqrt(45/5)$ $=$ $sqrt9$

Divide the variables

$sqrt(x^3) / sqrt(x^2)$ $=$ $sqrt((x^3)/(x^2))$ $=$ $sqrt(x)$

Combine the simplified divisions.

$=$ $sqrt(9)$ $xx$ $sqrt(x)$ Simplify

$=$ $3 xx sqrt(x)$

$=$ $3sqrt(x)$

$3sqrt(x)$

	$(\color(blue)(4)\color(red)(sqrt8)times\color(blue)(2)\color(red)(sqrt5))/(8sqrt20)$
$=$	$(\color(blue)(4times2)\color(red)(sqrt(8times5)))/(8sqrt20)$	Multiply the coefficients by each other and the surds by each other in the numerator
$=$	$(\color(blue)(8)\color(red)(sqrt(40)))/(8sqrt20)$
$=$	$sqrt40/sqrt20$	Simplify the coefficients
$=$	$sqrt(40/20)$	Rewrite and simplify the surds
$=$	$sqrt(2)$

	$(\color(blue)(8)\color(red)(sqrt3)times\color(blue)(5)\color(red)(sqrt6))/(4sqrt18)$
$=$	$(\color(blue)(8times5)\color(red)(sqrt(3times6)))/(4sqrt18)$	Multiply the coefficients by each other and the surds by each other in the numerator
$=$	$(\color(blue)(40)\color(red)(sqrt(18)))/(4sqrt18)$
$=$	$(10sqrt18)/sqrt18$	Simplify the coefficients
$=$	$10sqrt(18/18)$	Rewrite and simplify the surds
$=$	$10sqrt1$
$=$	$10$

	$(4sqrt(27)timessqrt(18))/(sqrt(48))$	Reduce the surds
$=$	$(4sqrt(9times3)timessqrt(9times2))/(sqrt(16times3))$	Simplify
$=$	$(12sqrt(3)times3sqrt(2))/(4sqrt(3))$
$=$	$(\color(blue)(12)\color(red)(sqrt(3))times\color(blue)(3)\color(red)(sqrt(2)))/(4sqrt(3))$	Multiply the coefficients by each other and the surds by each other in the numerator
$=$	$(\color(blue)(12times3)\color(red)(sqrt(3times2)))/(4sqrt(3))$
$=$	$(\color(blue)(36)\color(red)(sqrt(6)))/(4sqrt(3))$
$=$	$(9sqrt(6))/sqrt(3)$	Simplify the coefficients
$=$	$9sqrt(6/3)$	Rewrite and simplify the surds
$=$	$9sqrt(2)$

Multiply and Divide Surd Expressions

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Quiz summary

Information

1. Question

Nice Work!

Multiplication Property of Square Roots

Division Property of Square Roots

2. Question

Nice Work!

Multiplication Property of Square Roots

Division Property of Square Roots

3. Question

Nice Work!

Multiplication Property of Square Roots

Division Property of Square Roots

4. Question

Hint

Excellent!

Multiplication Property of Surds

5. Question

Hint

Exceptional!

Multiplication Property of Surds

6. Question

Hint

Great Work!

Division Property of Surds

Quizzes

$sqrt(5a^2) xx sqrt(12b^5)$	$=$	$sqrt(5 xx 12 xx a^2b^5)$
	$=$	$sqrt(60a^2b^5)$

$=$	$sqrt(4 xx 15 xx a^2 xx b^4 xx b)$
$=$	$sqrt4 xx sqrt15 xx sqrt(a^2) xx sqrt(b^4) xx sqrt(b)$
$=$	$2 xx sqrt15 xx a xx b^2 xx sqrt(b)$
$=$	$2 xx a xx b^2 xx sqrt15 xx sqrt(b)$	Simplify
$=$	$2ab^2sqrt(15b)$

$sqrt(7xy^2) xx 5sqrt(x)$	$=$	$5sqrt(7 xx x xx y^2 xx x)$
	$=$	$5sqrt(7 xx x^2y^2)$

$=$	$5 sqrt7 xx sqrt(x^2) xx sqrt(y^2)$	Simplify
$=$	$5sqrt7 xx x xx y$
$=$	$5xy sqrt7$

$=$	$sqrt(9)$ $xx$ $sqrt(x)$	Simplify
$=$	$3 xx sqrt(x)$
$=$	$3sqrt(x)$